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arXiv:1311.3147 · Journal of Physics Condensed Matter

A DFT+nonhomogeneous DMFT approach for finite systems

Alamgir Kabir, Volodymyr Turkowski, Talat Shahnaz Rahman

Published Mar 5, 2015• 0 citations
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Abstract

For reliable and efficient inclusion of electron-electron correlation effects in nanosystems we formulate a combined density functional theory/nonhomogeneous dynamical mean-field theory (DFT+DMFT) approach which employs an approximate iterated perturbation theory impurity solver. We further apply the method to examine the size-dependent magnetic properties of iron nanoparticles containing 11-100 atoms. We show that for the majority of clusters the DFT+DMFT solution is in very good agreement with experimental data, much better compared to the DFT and DFT+U results. In particular, it reproduces the oscillations in magnetic moment with size as observed experimentally. We thus demonstrate that the DFT+DMFT approach can be used for accurate and realistic description of nanosystems containing about hundred atoms.

DOI
10.1088/0953-8984/27/12/125601

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For reliable and efficient inclusion of electron-electron correlation effects in nanosystems we formulate a combined density functional theory/nonhomogeneous dynamical mean-field theory (DFT+DMFT) approach which employs an approximate iterated perturbation theory impurity solver. We further apply the method to examine the size-dependent magnetic properties of iron nanoparticles containing 11-100 atoms. We show that for the majority of clusters the DFT+DMFT solution is in very good agreement with experimental data, much better compared to the DFT and DFT+U results. In particular, it reproduces the oscillations in magnetic moment with size as observed experimentally. We thus demonstrate that the DFT+DMFT approach can be used for accurate and realistic description of nanosystems containing about hundred atoms.
For reliable and efficient inclusion of electron-electron correlation effects in nanosystems we formulate a combined density functional theory/nonhomogeneous dynamical mean-field theory (DFT+DMFT) approach which employs an approximate iterated perturbation theory impurity solver. We further apply the method to examine the size-dependent magnetic properties of iron nanoparticles containing 11-100 atoms. We show that for the majority of clusters the DFT+DMFT solution is in very good agreement with experimental data, much better compared to the DFT and DFT+U results. In particular, it reproduces the oscillations in magnetic moment with size as observed experimentally. We thus demonstrate that the DFT+DMFT approach can be used for accurate and realistic description of nanosystems containing about hundred atoms.
Nanostructures with open shell transition metal or molecular constituents host often strong electronic correlations and are highly sensitive to atomistic material details. This tutorial review discusses method developments and applications of theoretical approaches for the realistic description of the electronic and magnetic properties of nanostructures with correlated electrons. First, the implementation of a flexible interface between density functional theory and a variant of dynamical mean field theory (DMFT) highly suitable for the simulation of complex correlated structures is explained and illustrated. On the DMFT side, this interface is largely based on recent developments of quantum Monte Carlo and exact diagonalization techniques allowing for efficient descriptions of general four fermion Coulomb interactions, reduced symmetries and spin-orbit coupling, which are explained here. With the examples of the Cr (001) surfaces, magnetic adatoms, and molecular systems it is shown how the interplay of Hubbard U and Hund’s J determines charge and spin fluctuations and how these interactions drive different sorts of correlation effects in nanosystems. Non-local interactions and correlations present a particular challenge for the theory of low dimensional systems. We present our method developments addressing these two challenges, i.e., advancements of the dynamical vertex approximation and a combination of the constrained random phase approximation with continuum medium theories. We demonstrate how non-local interaction and correlation phenomena are controlled not only by dimensionality but also by coupling to the environment which is typically important for determining the physics of nanosystems.
In this lecture we give an introduction to theoretical description of strongly correlated materials based on dynamical mean-¿eld theory (DMFT) and its extensions.The goal of this theoretical construction is to retain the many-body aspects of local atomic physics within the extended solid.The effects of short-range non-local correlations within cluster extensions of the DMFT scheme, as well as long-range Àuctuations within the fully renormalized dual-fermion perturbation scheme are discussed extensively.Recent progress in the numerical solution of the DMFT effective quantum impurity problem within the recently developed continuous-time Quantum Monte Carlo schemes is reviewed.We then describe realistic extensions of this approach which combine the accuracy of ¿rst-principle Density-Functional Theory with the treatment of local many-body effects within DMFT.
Correlated electron systems exhibit a variety of intriguing emergent phenomena, including Mott physics, pseudogap behavior, and unconventional superconductivity. One of the most widely used numerical approaches for investigating these systems is dynamical mean-field theory (DMFT). This dissertation addresses two related problems: how to develop better quantum impurity solvers for DMFT and how to use DMFT results to gain a better understanding of correlated electron systems. The first part of this dissertation develops numerical methods for solving quantum impurity problems, which constitute the central computational task in DMFT calculations. In Chap. 4, we develop a method that combines a tensor-train numerical integration scheme with the inchworm hybridization expansion for quantum impurity problems. Benchmarks on spinless, single-orbital, and multi-orbital impurity models demonstrate the convergence of the Green’s functions to exact or reference results and identify the regimes in which tensor-train compression of Feynman diagrams and the inchworm expansion itself are effective. In Chap. 5, we introduce the concept of counterterms within the hybridization expansion and apply it to a bare hybridization expansion solver that relies on a sum-of-exponentials integration technique. Tests on spinless, multi-orbital, and realistic embedding impurity problems show that counterterms can significantly reduce the required perturbative order and improve the efficiency of hybridization-expansion calculations. The second part of this dissertation applies the cluster extension of DMFT to the single-band Hubbard model. In Chap. 6, we introduce a fluctuation decomposition for the self-energy that eliminates the Fierz ambiguity encountered in conventional fluctuation diagnostics of the Hubbard model. The resulting analysis shows that spin fluctuations make an important contribution to the pseudogap self-energy, while multi-boson contributions are also necessary for a complete description. In Chap. 7, we analyze the spin-fermion coupling and its role in d-wave pairing. Our calculations show that, for antinodal fermions in the pseudogap regime, their coupling to antiferromagnetic spin fluctuations is strongly enhanced relative to the non-interacting limit. A modified Bethe–Salpeter equation analysis further shows that this enhanced spin–fermion coupling boosts the spin-fluctuation-induced contribution to the d-wave pairing susceptibility.
In this thesis, we tackle various problems in strongly correlated electron systems, which can be addressed properly via the non-perturbative dynamical mean field theory (DMFT) approach using the continuous time quantum Monte Carlo method as an impurity solver. First, we revisit the old Nagaoka ferromagnetism problem in the U=oo Hubbard model and study the stability of the ferromagnetic state as a function of the temperature, the doping level, and the next-nearest-neighbor hopping t'. We then address the nature of the Mott transition in the two-dimensional Hubbard model at half-filling using cluster DMFT. Cluster DMFT can incorporate the short-range correlations beyond DMFT by extending the spatial range in which correlations are treated exactly to a finite cluster size. The non-local correlations reduce substantially the critical interaction U and modify the shape of the transition lines in the phase diagram. We then concentrate on the calculation of two-particle response functions from the ab initio perspective by means of computing the one-particle excitation spectrum using the combination of the density functional theory (DFT) and DMFT and extracting the two-particle irreducible vertex function from a local two-particle Green's function computed within DMFT. In particular, we derive the equations for calculating the magnetic/charge susceptibility and the pairing susceptibility in superconductivity. This approach is applied to the Hubbard model and the periodic Anderson model and we determine the phase diagram of magnetism and superconductivity in these models. We show that the superconducting phase is indeed stable near the magnetic phase where the pairing interaction mediated by spin fluctuations is dominantly enhanced. The non-local correlation effect to superconductivity is also discussed using the dual fermion approach and the dynamical vertex approximation. We finally apply the vertex function approach within DFT+DMFT to a Fe-based superconductor, BaFe2As2, and compute the dynamical magnetic susceptibility in this material. Our calculation results show a good agreement with the magnetic excitation spectra observed in a neutron scattering experiment. The response function calculation method derived in this thesis can capture both a localized and an itinerant nature of collective excitations in strongly correlated electron systems.
We present an efficient ab initio dynamical mean-field theory (DMFT) implementation for quantitative simulations in solids. Our DMFT scheme employs ab initio Hamiltonians defined for impurities comprising the full unit cell or a supercell of atoms and for realistic quantum chemical basis sets. We avoid double counting errors by using Hartree-Fock as the low-level theory. Intrinsic and projected atomic orbitals (IAO + PAO) are chosen as the local embedding basis, facilitating numerical bath truncation. Using an efficient integral transformation and coupled-cluster Green's function impurity solvers, we are able to handle embedded impurity problems with several hundred orbitals. We apply our ab initio DMFT approach to study a hexagonal boron nitride monolayer, crystalline silicon, and nickel oxide in the antiferromagnetic phase, with up to 104 and 78 impurity orbitals in the spin-restricted and unrestricted cluster DMFT calculations and over 100 bath orbitals. We show that our scheme produces accurate spectral functions compared to both benchmark periodic coupled-cluster computations and experimental spectra.